Showing papers in "Acta Mechanica in 1971"
TL;DR: In this article, the modified heat conduction equation is used to study plane harmonic waves in unbounded media as well as Rayleigh's surface waves propagating along a half-space consisting of linearly elastic materials that conduct heat.
Abstract: Maxwell's modified heat conduction equation is used to study plane harmonic waves in unbounded media as well as Rayleigh's surface waves propagating along a half-space consisting of linearly elastic materials that conduct heat. Explicit expressions are obtained for various parameters that characterize these waves. Relevant results of previous investigations are deduced as special cases.
193 citations
TL;DR: A generalization of the classical plasticity theories which accounts for the observed phenomenon of noncoincident yield and loading surfaces is proposed in this paper, where constitutive relations are developed for arbitrary hardening laws and detailed results are presented and applied for isotropically hardening materials.
Abstract: A generalization of the classical plasticity theories which accounts for the observed phenomenon of noncoincident yield and loading surfaces is proposed. Constitutive relations are developed for arbitrary hardening laws and detailed results are presented and applied for isotropically hardening materials.
68 citations
TL;DR: In this article, a rigorous derivation of the fundamental laws governing macroscopic flow of fluids in a porous medium is given within the framework of classical continuum mechanics and the resulting equations contain the continuity equation and the Euler equations of motion of hydrodynamics as well as Darcy's law as special cases.
Abstract: This paper is devoted to a rigorous derivation of the fundamental laws governing the macroscopic flow of fluids in a porous medium. The derivation is given within the framework of classical continuum mechanics and the resulting equations contain the continuity equation and the Euler equations of motion of hydrodynamics as well as Darcy's law as special cases.
38 citations
TL;DR: In this paper, two general solutions to the linear theory of micropolar thermoelasticity are presented; one representation involves deformation potentials, the other employs stress-functions.
Abstract: Two general solutions to the linear theory of micropolar thermoelasticity are presented; one representation involves deformation potentials, the other employs stress-functions. The two representations are used to analyze the thermal stresses and thermal couple stresses in the vicinity of a cavity and a rigid inclusion during uniform heat flow.
36 citations
TL;DR: In this article, the boundary-layer equations are solved for the case of two-dimensional flow of a second-order viscoelastic fluid near a stagnation point, and it is shown that the effect of visco-elasticity is not only to increase the wall-shear stress but also to cause oscillations in the velocity profile.
Abstract: The boundary-layer equations are solved for the case of two-dimensional flow of a second-order viscoelastic fluid near a stagnation point. It is shown that the effect of viscoelasticity is not only to increase the wall-shear stress but also to cause oscillations in the velocity profile. It is further shown that the constitutive equation for the second-order viscoelastic fluid is not applicable to the analysis of stagnation point flow for Weissenberg numbers greater than approximately 0.32.
27 citations
TL;DR: Sloshing liquid natural frequencies change in cylindrical shell by movable devices, considering immersed thin elastic plate effect as mentioned in this paper, where the authors consider the elasticity of the shell.
Abstract: Sloshing liquid natural frequencies change in cylindrical shell by movable devices, considering immersed thin elastic plate effect
22 citations
TL;DR: In this article, the behavior of an incompressible and nonviscous liquid with a free surface in a uniformly fast rotating infinitely long elastic circular cylinder is treated, and the natural frequencies of the liquid in a rigid container, as well as the response of liquid to forced rigid and elastic container wall excitations are presented.
Abstract: The behavior of an incompressible and nonviscous liquid with a free surface in a uniformly fast rotating infinitely long elastic circular cylinder is treated. The natural frequencies of the liquid in a rigid container, as well as the response of the liquid to forced rigid and elastic container wall excitations are presented. Furthermore, the determination of the hydroelastic spin-slosh problem is presented, since the elasticity of the spinning container wall may considerably influence the magnitude of the coupled frequencies of the liquid-structure system.
22 citations
TL;DR: In this paper, the steady laminar viscous hypersonic flow of an electrically conducting fluid in the region of the stagnation point of an insulating blunt body in the presence of a radial magnetic field is studied by similarity solution approach, taking into account the variation of the product of density and viscosity across the boundary layer.
Abstract: In this paper, the steady laminar viscous hypersonic flow of an electrically conducting fluid in the region of the stagnation point of an insulating blunt body in the presence of a radial magnetic field is studied by similarity solution approach, taking into account the variation of the product of density and viscosity across the boundary layer. The two coupled non-linear ordinary differential equations are solved simultaneously using Runge-Kutta-Gill method. It has been found that the effect of the variation of the product of density and viscosity on skin friction coefficient and Nusselt number is appreciable. The skin friction coefficient increases but Nusselt number decreases as the magnetic field or the total enthalpy at the wall increases.
15 citations
TL;DR: The effect of magnetic damping on the stability of equilibrium of some circulatory elastic systems is examined in this paper, where a simple system with two degrees of freedom is considered, and a destabilization is found to be caused by the magnetic field.
Abstract: The effect of a type of magnetic damping on the stability of equilibrium of some circulatory elastic systems is examined. A simple system with two degrees of freedom is considered first, and a destabilization is found to be caused by the magnetic field. The nature of the destabilization, however, is not identical to that caused by internal viscous damping. The differences and similarities between the two effects are discussed, and the results are also compared with those of linear external viscous damping. A continuous cantilever bar subjected to a follower force at its free end is then examined. It is found that the critical load is independent of the strength of the magnetic field, and is considerably lower than the corresponding critical load in the absence of a magnetic field. Finally, the continuous cantilever is treated approximately by Galerkin's procedure and also by using a two-degree-of-freedom model of the cantilever; the results obtained are qualitatively the same.
11 citations
TL;DR: In this paper, the transient response of a uniformly expanding, impulsively loaded, long cylinder is obtained in terms of elementary functions for an elastic perfectly-plastic von Mises material.
Abstract: The transient response of a uniformly expanding, impulsively loaded, long cylinder is obtained in terms of elementary functions for an elastic perfectly-plastic von Mises material. The solution is obtained by utilizing a linearizing assumption on the plastic flow behavior. It is generally shown that differences in elastic-plastic response of (plane strain) long cylinders with various values of Poisson's ratio,v, are slight over a wide range ofv. However, differences in response between long cylinders and (plane stress) rings undergoing plasticity are quite significant.
10 citations
TL;DR: In this article, the linear eigenvalue problem is solved in closed form for heterogeneous isotropic circular plates with clamped or simply supported circumference, and invariant buckling parameters are obtained which enable optimization.
Abstract: Axisymmetric nonlinear buckling equations are introduced for thin elastic circular plates composed of isotropic or orthotropic layers, uniformly compressed in the radial direction. The linear eigenvalue problem is solved in closed form for heterogeneous isotropic circular plates with clamped or simply supported circumference. Invariant buckling parameters are obtained which enable optimization. Several numerical examples are shown.
TL;DR: In this paper, the Stromung einer inkompressiblen, zahen Flussigkeit zwischen zwei parallelen Scheiben, die eine zentralale Bohrung haben und mit gleicher Winkelgeschwindigkein rotieren, theoretisch und experimentell untersucht.
Abstract: Es wird die Stromung einer inkompressiblen, zahen Flussigkeit zwischen zwei parallelen Scheiben, die eine zentrale Bohrung haben und mit gleicher Winkelgeschwindigkeit rotieren, theoretisch und experimentell untersucht. Fur die laminare Stromung habenBreiter undPohlhausen eine Losung angegeben. Im turbulenten Fall wird die Stromung mit Hilfe des Impulssatzes der Grenzschichttheorie berechnet. Beide Rechnungen werden durch Ausmessen der Geschwindigkeitsverteilung uber dem Spaltquerschnitt mittels der Hitzdrahttechnik uberpruft und in ihrer Brauchbarkeit bestatigt. Im Ubergangsgebiet zwischen laminarer und turbulenter Stromungsform ergeben sich relativ zu den umlaufenden Scheiben stehende, spiralige Wirbel. Die Untersuchungen haben praktische Bedeutung, da die beschriebene Anordnung des Scheibenpaares identisch ist mit dem Spaltelement einer Reibungspumpe nachTesla.
TL;DR: In this article, a theoretical analysis for the membrane and bending stresses around an elliptic hole in an infinitely long, thin circular cylindrical shell is presented, where the shell is loaded by a uniformly distributed bending moment around the elliptic cutout.
Abstract: A theoretical analysis is presented for the membrane and bending stresses around an elliptic hole in an infinitely long, thin circular cylindrical shell The shell is loaded by a uniformly distributed bending moment around the elliptic cutout The method of solution is a perturbation technique and the results obtained are valid, if the hole is small in size compared to the shell
TL;DR: An approximate theory for the vibration of non-homogeneous, anisotropic plates is presented in this article, where the equations are derived by use of the asymptotic integration of the elasticity equations.
Abstract: An approximate theory for the vibration of non-homogeneous, anisotropic plates is presented. The equations are derived by use of the asymptotic integration of the elasticity equations. Although use of this method leads to field equations of various orders, only the first approximation equations are derived here. The application to layered plates is also shown.
TL;DR: In this paper, the finite part of an integral (FPI) problem is considered in the context of perturbed heterogeneous shear flow, where the eigenfunctions corresponding to the continuous spectrum of eigenvalues are generalized functions rather than ordinary functions.
Abstract: The initial-value problem corresponding to a perturbed heterogeneous shear flow is considered. When the normal-mode method is applied, the solution of the problem is most easily obtained by introducing the concept “the finite part of an integral”. In fact it means that the eigen-functions corresponding to the continuous spectrum of eigenvalues are generalized functions rather than ordinary functions.
TL;DR: In this paper, a flussigkeitsgefullten Ringspalt zweier konzentrischer Zylinder, von denen der innere rotiert, treten die abwechselnd rechts und links drehenden Taylor-Wirbel auf.
Abstract: Im flussigkeitsgefullten Ringspalt zweier konzentrischer Zylinder, von denen der innere rotiert, treten die abwechselnd rechts und links drehenden Taylor-Wirbel auf. Betrachtet man die durch Aluminium-Pulver sichtbar gemachte Stromung genauer, so stellt man fest, das bei diesen Ringwirbeln die Bereiche mit Ruckstromung ins Innere wesentlich dunkler erscheinen als diejenigen Bereiche, in denen die Stromung zur Ausenwand hin erfolgt. Dieser Effekt ist uberraschend, man erwartet zunachst eine symmetrische Helligkeitsverteilung.
TL;DR: In this paper, it was shown that the Stewartson model is not the correct one and that a flow of the Taylor column type is present, and experimental evidence is presented in Part II which confirms the existence of this latter phenomenon.
Abstract: Using the model suggested byStewartson (1957) in which for largeR the effect of the sphere is assumed to be local, an attempt is made in Part I of this paper to find higher order terms. The analysis suggests that this model is not the correct one and that a flow of the Taylor column type is present. Experimental evidence is presented in Part II which confirms the existence of this latter phenomenon.
TL;DR: The extended Kantorovich method was used in this article to analyze the steady flow of a viscous, electrically conducting fluid through a perfectly insulated rectangular duct under a uniform, arbitrarily oriented, externally applied magnetic field.
Abstract: The extended Kantorovich method developed byA. D. Kerr and recently applied to the solution of a clamped plate byA. D. Kerr andH. Alexander, is used in the present paper to analyze the steady flow of a viscous, electrically conducting fluid through a perfectly insulated rectangular duct under a uniform, arbitrarily oriented, externally applied magnetic field. It is shown that the generated solution is independent of the choice of initial function, and that the convergence of the iterative procedure is very rapid. The obtained solution exhibits good correlation with the exact solution for small values of the Hartmann number. The inaccuracy at high Hartmann numbers is shown to be a result of a shortcoming in the method as it is presently applied.
TL;DR: In this article, an initial value investigation into the two dimensional linearized problem of surface wave propagation in a fluid of limited and unlimited depth due to harmonically oscillating sources has been made.
Abstract: An initial value investigation into the two dimensional linearized problem of surface wave propagation in a fluid of limited and unlimited depth due to harmonically oscillating sources has been made. An asymptotic analysis of the problem has been carried out in a considerable detail for a clear understanding of both the steady state and the transient solutions. The limiting behaviour of the asymptotic solution as timeT tends to infinity has also been given due attention. Lastly, the corresponding steady state solution is obtained as a limiting case, and a discussion about the wave motions is made in some detail.
TL;DR: In this paper, the title problem for the Oseen-like model of Part I is solved exactly for the realistic case of flow limited to a channel with forward moving walls, where the motion is governed by two simultaneous Wiener-Hopf equations, which uncouple when the oncoming flow is uniform.
Abstract: The title problem for the Oseen-like model of Part I is solved exactly for the realistic case of flow limited to a channel with forward moving walls. The motion is governed by two simultaneous Wiener-Hopf equations, which uncouple when the oncoming flow is uniform. Then computation of the flow pattern is relatively easy and the nature of cross flow is clear. In particular, the occurrence of backflow (with its attached vortex) is examined. For true shear flow explicit formulas could only be obtained when the viscosity is small, but this is sufficient to prove the main result: second-order boundary-layer theory correctly gives the shear stress on the plate near the leading edge provided there is no total cross flux.
TL;DR: In der vorliegenden Arbeit werden Moglichkeiten untersucht, statische and geometrische Feldgrosen linear-elastischer Probleme naherungsweise zu berechnen bei gleichzeitiger Angabe eines maximalen Fehlers as mentioned in this paper.
Abstract: In der vorliegenden Arbeit werden Moglichkeiten untersucht, statische und geometrische Feldgrosen linear-elastischer Probleme naherungsweise zu berechnen bei gleichzeitiger Angabe eines maximalen Fehlers. Dazu benutzt man sowohl fur den unbekannten Zustand wie fur einen Greenschen Zustand, der durch die zu bestimmende Feldgrose definiert wird, Vergleichszustande, die entweder die geometrischen oder die statischen Bedingungen erfullen. Durch Ansatze mit unbestimmten Koeffizienten und Minimierung der Fehlerenergie lassen sich die Fehlerschranken soweit verkleinern, bis eine fur technische Zwecke genugende Genauigkeit erreicht wird.
TL;DR: In this paper, the authors analyze and classify motions of continuous bodies with the aid of elementary concepts taken from group and lattice theory, such as d'Alembert, homogeneous, and circulation-preserving motions.
Abstract: Motions of continuous bodies are analyzed and classified in regard of kinematical aspects with the aid of elementary concepts taken from group and lattice theory. Venn-Euler and Hasse diagrams serve for illustration. The groups of d'Alembert, homogeneous, and circulation-preserving motions cover chains of several subgroups, among which simple shearing and extensional motions are chosen as atoms. It appears that extensional (in contradistinction to shearing) motions can be defined as irrotational homogeneous d'Alembert motions with a distinct demarcation in the group lattice. Kinematical and dynamical discussions aim above all at consequences for extensional viscometry, which will form the main subject of successive contributions.
TL;DR: In this article, the constitutive relations for a mixture of two simple materials with fading memory are derived, based on the thermodynamic theory proposed by Green and Naghdi [1].
Abstract: Constitutive relations for a mixture of two simple materials with fading memory are derived, based on the thermodynamical theory proposed byGreen andNaghdi [1]. Special attention is devoted to a mixture of two simple fluids the motion of which has been slow in recent past.
TL;DR: In this paper, the problem of torsional oscillations set up in an elastic stratum, one face of which is rigidly secured, by a rigid circular disk which is attached to the free surface of the material and which performs simple harmonic oscillations about its axis is solved after reducing it to the solution of a Fredholm Integral Equation of the second kind.
Abstract: This paper is concerned with straightforward solution of the problem of torsional oscillations set up in an elastic stratum, one face of which is rigidly secured, by a rigid circular disk which is attached to the free surface of the material and which performs simple harmonic oscillations about its axis. The problem has been solved after reducing it to the solution of a Fredholm Integral Equation of the second kind.
TL;DR: In this article, numerische Losungen with Hilfe eines Differenzenverfahrens gewonnen are discussed in abhangigkeit von der Reynoldsschen Zahl and vom Durchflus diskutiert.
Abstract: Gegenstand der vorliegenden Arbeit ist die Berechnung des Stromungsfeldes in einem inkompressiblen Medium zwischen einer rotierenden Scheibe und einer festen Wand, die kreisformige Offnungen konzentrisch zur Rotationsachse besitzen. Der Spalt zwischen den Platten ist klein im Vergleich zum Offnungsradius. Ausgehend von vereinfachten Navier-Stokesschen Gleichungen werden numerische Losungen mit Hilfe eines Differenzenverfahrens gewonnen. Die Geschwindigkeitsprofile werden in Abhangigkeit von der Reynoldsschen Zahl und vom Durchflus diskutiert.
TL;DR: In this article, an integral equation method is applied to the solution of the transonic small disturbance equation for finite wings in subsonic flows, and the spanwise influence of the nonlinear compressibility sources is expressed in terms of Bessel and related functions.
Abstract: An integral equation method is applied to the solution of the transonic small disturbance equation for finite wings in subsonic flows. The spanwise influence of the nonlinear compressibility sources is expressed in terms of Bessel and related functions. Additional nonlinear compressibility effects are considered two dimensional. Numerical results for high aspect ratio wings approach correctly the corresponding planar values. Results obtained for slender pointed small aspect ratio wings are transformed to the solution of the equivalent body of revolution and are then favorable compared with the solution given by the method of local linearization.
TL;DR: In this paper, a plane, laminar two-phase jet flow is considered, where the two phase medium in the jet consists of small spherical solid particles suspended in an incompressible carrier fluid and the derived linear equations are solved by Laplace transforms.
Abstract: A plane, laminar two-phase jet flow is considered, where the two-phase medium in the jet consists of small spherical solid particles suspended in an incompressible carrier fluid The development of the jet flow is studied in the presence of a moving free stream, containing no particles and alined with the jet. Diffusion of particles as well as the effect of carrier- and particle-phase viscosity is taken into account. A perturbation analysis is performed based on small particle concentration and small velocity differences between jet- and free-stream speed. Accordingly, the derived linear equations are solved byLaplace transforms. Resutiing expressions for particle velocity profiles contain two parameters. One of these is the ratio of the carrierReynolds number and the particle velocity relaxation parameter, and the other is the ratio of the particle diffusion coefficient and the carrier fluid viscosity. It is shown that both parameters can have a profound influence on the solution.
TL;DR: In this article, the components of the finite displacements, rotations and stress resultants of a thin elastic rod with inextensible axis were determined by using three-dimensional kinematics of a rigid body.
Abstract: By using three-dimensional kinematics of a rigid body, the components of the finite displacements, rotations and stress resultants of a thin elastic rod with inextensible axis are determined.
TL;DR: In this article, the static problem of plane strain in the linear theory of micropolar thermoelasticity assuming that heat sources are absent is considered and a method for the reduction of the problem to an isothermal one with certain known boundary conditions is given.
Abstract: We consider the static problem of plane strain in the linear theory of micropolar thermoelasticity assuming that heat sources are absent. We give a method for the reduction of the thermoelastic problem to an isothermal one with certain known boundary conditions. In the case of a multiply connected region this leads to the notion of dislocations.
TL;DR: In this article, two novel types of extensional viscometers are proposed under the designations closed-end and open-end hose viscometer, which form an elastically extensible cover of a prolate circular cylinder shape, to hold an incompressible fluid specimen for investigation, especially under forced oscillations.
Abstract: After a historical survey on the evolution of extensional viscometry, two novel types of extensional viscometers are proposed under the designations closed-end and open-end hose viscometer. The hose, which forms an elastically extensible cover of a prolate circular cylinder shape, is to hold an incompressible fluid specimen for investigation, especially under forced oscillations. The measurement of the first type concerns the axial force of the specimen in a thin-walled hose; the measurement of the second type concerns the radial traction of the specimen in a thick-walled hose. Fundamental design features and a mathematical treatment under ideal conditions are set forth for eventually showing how to unroll an informative (though expensive) program of viscometry on the base of harmonic Fourier analysis. In an appendix, the ascertainment of material coefficients is exemplified on specific constitutive assumptions so as to suggest analogously handling other instances on demand.